PHYSICS

DROPPER JEE

NEWTON’S LAWS
OF MOTION
 VIDYAPEETH
NEWTON’S LAWS OF MOTION
DPP-1 (JPP/019)
[Newton’s First Law of Motion, Inertia and Mass, Momentum,
Mathematical Formulation of Second Law]
1. When a train stops suddenly, passengers 3. A boy sitting on the topmost berth in the
in the train feel an instant jerk in the compartment of a train which is just going
forward direction because to stop on a railway station, drops an apple
(A) The back of seat suddenly pushes aiming at the open hand of his brother
the passengers forward sitting vertically below his hands at a
(B) Inertia of rest stops the train and
distance of about 2 meter. The apple will
takes the body of passengers
fall
forward
(A) Precisely on the hand of his brother
(C) Upper part of the body continues to
(B) Slightly away from the hand of his
be in the state of motion whereas the
lower part of the body in contact with brother in the direction of motion of
seat remains at rest the train
(D) Nothing can be said due to (C) Slightly away from the hand of his
insufficient data brother in the direction opposite to
the direction of motion of the train
2. A man getting down a running bus falls
(D) None of the above
forward because
(A) Due to inertia of rest, road is left 4. There are two bodies A & B of same
behind and man goes forward mass. Body A is at rest while body B is
(B) Due to inertia of motion, upper part
undergoing uniform motion, which is
of body continues to be in motion in
correct statements?
forward direction while feet come to
(A) Inertia of A > inertia of B.
rest as soon as they touch the road
(B) Inertia of B > inertia of A.
(C) He leans forward as a matter of habit
(D) Of the combined effect of all the (C) Inertia of A = inertia of B.
three factors stated in (A), (B) and (D) Either A, B or C depending upon the
(C) shape of body.

(2)
5. When an object is at rest 9. An object of mass 10 kg is moving at a
(A) Force is required to keep it in rest constant velocity of 10 m/s. A constant
state force then acts for 4 seconds on the object
(B) No force is acting on it and gives it a speed of 2m/s in opposite
(C) A large number of forces may be direction. The force acting on in it, is
acting on it which balance each (A) 10 N (B) 30 N
other (C) 20 N (D) 40 N
(D) It is in vacuum
10. A particle of mass 'm' originally at rest, is
6. If the force of gravity suddenly subjected to a force whose direction is
disappears: constant but whose magnitude varies
(A) The mass of all bodies will become according to the relation
zero 2 t 
F  F0t  – 2  ,where F0 and T are
(B) The weight of all bodies will T T 
become zero constant. Then speed of the particle after
(C) Both mass and weight of all bodies a time 2T is:
will become zero 3F0 4 F0
(A) T (B) T
(D) Neither mass nor weight of all 4m 3m
bodies will become zero 2F0 F
(C) T (D) 0 T
m m
7. A rider on horse back falls when horse
starts running all of a sudden because 11. A force of 10 N is applied to a mass of 10
(A) Rider is taken back gm for 10 seconds. The change of
(B) Rider is suddenly afraid of falling momentum in kgm / sec units will
(C) Inertia of rest keeps the upper part of be_______.
body at rest whereas lower part of
the body moves forward with the 12. Assertion: Newton's first law is
horse contained in Newton’s second law.
(D) None of the above Reason: Action and reaction act on the
same body.
8. A block of metal weighing 5 kg is resting (A) Both Assertion & Reason are True
on a frictionless plane. It is struck by a jet & the Reason is a correct
releasing water at a rate of 2 kg/ sec and explanation of the Assertion.
at a speed of 4 m/s. The initial (B) Both Assertion & Reason are True
acceleration of the block will be: but Reason is not a correct
(A) 1.6 m/s² explanation of the Assertion.
(B) 20 m/s² (C) Assertion is True but the Reason is
(C) 2.5 m/s² False.
(D) None of the above (D) Both Assertion & Reason are False.

(3)
 DPP-2 (JPP/020)
[Impulse, Application of Newton’s Second Law of Motion, Applications of
Third Law, Conservation of Linear Momentum]
1. A jet engine works on the principle of 5. A particle of mass m strikes a wall with
(A) Conservation of mass speed v at an angle 30° with the wall
(B) Conservation of energy elastically as shown in the figure. The
(C) Conservation of linear momentum magnitude of impulse imparted to the ball
(D) Conservation of angular momentum by the wall is

2. If n balls hit elastically and normally on a

surface per unit time and all balls of mass
m are moving with same velocity u, then
force on surface is
(A) mun (B) 2 mun
1
(C) mu2n (D) mu2n (A) mv (B) mv/2
2
(C) 2 mv (D) 3 mv
3. A ball of mass 50 g is dropped from a
height of 20 m. A boy on the ground hits
6. A force of (6 iˆ + 8 ĵ ) N acted on a body
the ball vertically upwards with a bat with
an average force of 200 N, so that it of mass 10 kg. The displacement after 10
attains a vertical height of 45 m. The time sec, if it starts from rest, will be –
for which the ball remains in contact with (A) 50 m along tan–1 4/3 with x axis
the bat is [Take g = 10 m/s2]
(B) 70 m along tan–1 3/4 with x axis
(A) 1/20th of a second
(B) 1/40th of a second (C) 10 m along tan–1 4/3 with x axis
(C) 1/80th of a second (D) None
(D) 1/120th of a second
7. A body of mass M at rest explodes into
4. In which of the following graphs, the total
three pieces, two of which of mass M/4
change in momentum is zero?
each are thrown off in perpendicular
directions with velocities of 3 m/s and
4m/s respectively. The third piece will be
(A) (B)
thrown off with a velocity of
(A) 1.5 m/s
(B) 2.0 m/s
(C) (D (C) 2.5 m/s
(D) 3.0 m/s

(4)
8. A bullet is fired from a gun. The force on 10. A 100 g iron ball having velocity 10 m/s
the bullet is given by F = 600 – 2 × 10 t,
5 collides at an angle 30° with a wall and
rebounds at the same angle. If the period
where F is in newton and t in seconds. of contact between the ball and wall is 0.1
The force on the bullet becomes zero as second, then the force experienced by the
soon as it leaves the barrel. What is the wall is ____________ N.

average impulse imparted to the bullet? 11. A player caught a cricket ball of mass 150
(A) 9 Ns (B) Zero gm moving at a rate of 20 m/s. If the
(C) 0.9 Ns (D) 1.8 Ns catching process is completed in 0.1 s,
then the force of the blow exerted by the
9. The magnitude of the force (in newton) ball on the hands of the player is
acting on a body varies with time t (in (A) 10 N
microseconds) as shown in fig. AB, BC, (B) 20 N
(C) 30 N
and CD are straight line segments. The
(D) 40 N
magnitude of the total impulse of the
force on the body from t = 4 s to t = 16 12. Assertion: Aeroplanes always fly at low
s is altitudes.
Reason: According to Newton’s third
law of motion, for every action there is an
equal and opposite reaction.
(A) Both Assertion & Reason are True
& the Reason is a correct
explanation of the Assertion.
(B) Both Assertion & Reason are True
but Reason is not a correct
(A) 5 × 10– 4 N.s explanation of the Assertion.
(B) 5 × 10– 3 N.s (C) Assertion is True but the Reason is
(C) 5 × 10– 5 N.s False.
(D) 5 × 10– 2 N.s (D) Both Assertion & Reason are False.

(5)
 DPP-3 (JPP/021)
[Laws of Motion Applied to Systems, Free Body Diagram]
1. A bullet of mass 40 g is fired from a gun 3. Consider the three cases given in figures
of mass 10 kg. If velocity of bullet is 400 shown. Assume the friction to be absent
m/s, then the recoil velocity of the gun everywhere and the pulleys to be light;
will be the string connecting the blocks to other
block or fixed vertical wall to be light and
(A) 1.6 m/s in the direction of bullet
inextensible. Let TA, TB and TC be the
(B) 1.6 m/s opposite to the direction of
tension in the strings in figure A, figure B
bullet
and figure C respectively. Then pick the
(C) 1.8 m/s in the direction of bullet correct comparison between the given
(D) 1.8 m/s opposite to the direction of tensions (for the instant shown) from
bullet options below.

2. A helicopter is moving to the right at a

constant horizontal velocity. It
experiences three forces Fgravitational , Fdrag

and force on it caused by rotor Frotor .

Which of the following diagrams can be
correct free body diagram representing
forces on the helicopter?

direction of motion (A) TA = TB = TC (B) TB = TC < TA

(C) TA < TB < TC (D) TB < TC < TA

4. Two weights W1 and W2 in equilibrium and

(A)
at rest are suspended as shown in figure.
W
Then the ratio 1 is:
W2
(B)

(C)

(A) 5/4
(D) (B) 4/5
(C) 8/5
(D) none of the these

(6)
5. Three blocks with masses m, 2m and 3m 8. Three blocks of masses 4 kg, 2 kg and 1
are connected by strings, as shown in the kg respectively are in contact on a
figure. After an upward force F is applied frictionless table as shown in the figure.
on block m, the masses moves upward at
constant speed v. What is the net force on If a force of 14 N is applied on the 4 kg
the block of mass 2m? block, the contact force between the 4 kg
(g is the acceleration due to gravity) and the 2 kg block will be

(A) 2 N (B) 6 N
(C) 8 N (D) 14 N

9. A spherical ball of mass m = 5 kg rests

(A) 6 mg (B) zero between two planes which make angles
(C) 2 mg (D) 3 mg of 30° and 45° respectively with the
horizontal. The system is in equilibrium.
6. In the given arrangement, n number of
equal masses are connected by strings of Find the normal forces exerted on the ball
negligible masses. The tension in the by each of the planes. The planes are
string connected to nth mass is smooth.

mMg mMg
(A) (B)
nm  M nmM
mMg
(C) mg (D) (A) N45 = 96.59 N, N30 = 136.6 N
m  nM
(B) N30 = 96.59 N, N45 = 136.6 N
7. A body of mass 10 kg is suspended by (C) N45 = 136.6 N, N30 = 96.56 N
two massless strings making angles 45°
(D) None of these
and 30° with horizontal as shown in the
figure, then
10. Consider the system as shown in the
figure.
The pulley and the string are light, and all
the surfaces are frictionless. The tension
in the string is ______N. (g = 10 m/s2)
(A) 2T1  3T2  0
(B) 2T1  3T 2  0
(C) 2T1  3T2  0
(D) 2T1  3T2  0

(7)
11. Find the tension in the string AB loaded
with weight W at the middle, when AB is
horizontal:

(A) zero (B) W

(C) W/2 (D) infinity

12. In the figure, at the free end of the light

string, a force F is applied to keep the
suspended mass of 18 kg at rest. Then the
force exerted by the ceiling on the system
(assume that the string segments are
vertical and the pulleys are light and
smooth) is (g = 10 m/s2)

(A) 180 N (B) 360 N

(C) 120 N (D) 240 N

(8)
 DPP-4 (JPP/022)
[Laws of Motion Applied to Systems, Free Body Diagram]
1. Force of 3N acts on a system of two blocks 4. Two smooth spheres each of radius 5 cm
of mass 2 kg and 1 kg as shown in figure. and weight W rest one on the other inside a
Contact force between the blocks is: fixed smooth cylinder of radius 8 cm. The
reactions between the spheres and the
reaction applied by the wall on spheres is:

(A) 1 N (B) 2 N
(C) 3 N (D) 0

2. As shown below, two blocks with masses

m and M (M > m) are pushed by a force F
in both case I and Case II. The surface on (A) W/4 and 3W/4 (B) W/4 and W/4
which blocks lie, is horizontal and (C) 5W/4 and 3W/4 (D) W and W
frictionless. Let RI be the force that m exerts
on M in case I and RII be the force that m 5. A 50 kg person stands on a 25 kg platform.
exerts on M in case II. Which of the He pulls on the rope which is attached to
following statements is true? the platform via the frictionless pulleys as
shown in the figure. The platform moves
upward at a steady rate if the force with
which the person pulls the rope is _____ N.
(A) RI = RII and is not equal to zero or F
(B) RI = RII = F
(C) RI < RII
(D) RI > RII

3. Four identical metal butterflies are hanging

from a light string of length 5l at equally
placed points as shown. The ends of the
string are attached to a horizontal fixed
support. The middle section of the string is 6. Two masses M1 to M2 connected by means
horizontal. The relation between the angle of a string which is made to pass over light,
1 and 2 is given by  smooth pulley are in equilibrium on a fixed
smooth wedge as shown in figure. If θ = 60°
and α = 30°, then the ratio of M1 to M2 is

(A) sin 1 = 2 sin 2

(B) 2 cos 1 = sin 2
(C) tan 1 = 2 tan 2
(A) 1 : 2 (B) 2 : 3
(D) 2 < 1 and no other conclusion can be
derived (C) 1 : 3 (D) 3:1

(9)
7. A body of mass 5 kg is suspended by the 10. In the figure shown, surface is frictionless.
strings making angles 60° and 30° with the Forces are applied as shown in figure, then
horizontal –
find tension T2.

250
(A) N
3
(a) T1 = 25 N (b) T2 = 25 N
190
(c) T1 = 25√3 N (d) T2 = 25√3 N (B) N
3
(A) a, b (B) a, d
(C) c, d (D) b, c (C) 90 N
(D) 50 N
8. The pulleys and string shown in the figure
are smooth and are of negligible mass. For
the system to remain in equilibrium, the 11. In the given diagram, the tension in string
angle  should be C is:

(A) 0° (B) 30° (A) 100 N (B) 70.7 N

(C) 45° (D) 60° (C) 141 N (D) 200 N
9. Three identical masses each of mass 4 kg
are connected by massless inextensible 12. Assertion: A body can be at rest even when
strings. The string joining A and B passes it is under the action of any number of
over a massless frictionless pulley as shown external forces.
in figure. The tension in the string
Reason: Vector sum of all the external
connecting mass B and C is
forces on a body may be zero.
(A) If both Assertion & Reason are True &
the Reason is a correct explanation of
the Assertion.
(B) If both Assertion & Reason are True
but Reason is not a correct explanation
of the Assertion.
(C) If Assertion is True but the Reason is
False.
(A) 40 N (B) 20 N (D) If Assertion is False but Reason is
(C) 16 N (D) 32 N True.

(10)
 DPP-5 (JPP/023)
[Problems Involving Constraint Relation]
1. In the figure shown, find out the value of  3. Calculate the acceleration of the block B in
[assume string to be tight] the shown figure, assuming the surfaces
and the pulleys P1 and P2 are all smooth and
pulleys and string and light.

3
(A) tan 1
4
3F
4 (A) a  m/s 2
(B) tan 1 20m
3
3F
3 (B) a  m/s 2
(C) tan 1 21m
8
(D) None of these 2F
(C) a  m/s 2
21m
2. In the given arrangement, mass of the block 3F
(D) a  m/s 2
is M and the surface on which the block is 18m
placed is smooth. Assuming all pulleys to
be massless and frictionless, strings to be
inelastic and light, R1, R2 and R3 to be light 4. Block A is moving away from the wall at a
supporting rods, then acceleration of point speed v and acceleration a.
‘P’ will be (A is fixed)

(A) 0 (A) Velocity of B is v with respect to A.

(B)  (B) Acceleration of B is a with respect to
4F A.
(C) (C) Acceleration of B is 4a with respect to
M
2F A.
(D)
M

(11)
 (D) Acceleration of B is 17a with respect 1 3
(A) m/s (B) m/s
to A. 2 4
5. The vertical displacement of block A in 1
(C) m/s (D) 1 m/s
t2 4
meter is given by y  where t is in 8. Find the velocity of the hanging block if the
4
second. Calculate the downward velocities of the free ends of rope are as
acceleration aB of block B. indicated in the figure.

(A) 3/2 m/s (B) 3/2 m/s

(C) 1/2 m/s (D) 1/2 m/s
(A) 2 m/s2 (B) 1 m/s2
(C) 4 m/s2 (D) 9 m/s2 9. Find out the magnitude of net force exerted
6. In the arrangement shown in figure the ends by the pulley on the rod R1
P and Q of an unstretchable string move
downwards with uniform speed U. Pulleys
A and B are fixed. Mass M moves upwards
with a speed
A   B

P M Q
(A) 2 F
(A) 2U cos  (B) U cos  (B) F
2U U (C) 2 2F
(C) (D)
cos  cos  F
(D)
2
7. Find velocity of ring B (VB) at the instant
shown. The string is taut and inextensible.
10. At a given instant, A is moving with
velocity of 5 m/s upwards. What is velocity
of B (in m/s) at that time?

(12)
 (A) 6 m/s
(B) 12 m/s
(C) 10 m/s
(D) 20 m/s
12. Assertion: String can never remain horizontal,
when loaded at the middle, howsoever large the
tension may be.
Reason: For horizontal string, angle with
W W
vertical,  = 90º, T = = = .
11. System is shown in the figure. Velocity of 2cos  2cos90º
sphere A is 9 m/s. The speed of sphere B is (A) Both Assertion and Reason are true,
and Reason is the correct explanation
of Assertion.
(B) Both Assertion and Reason are true
but Reason is not the correct
explanation of Assertion.
(C) Assertion is true but Reason is false.
(D) Assertion is false but Reason is true.

(13)
 DPP-6 (JPP/024)
[Pseudo force, Spring Force, Apparent Weight]
1. A pendulum bob is suspended in a Car 3. A block of mass m is placed on a smooth
moving horizontally with acceleration ‘a’. inclined wedge ABC of inclination  as
The angle the string will make with vertical shown in the figure. The wedge is given an
is acceleration ‘a’ towards the right. The
a relation between a and  for the block to
remain stationary on the wedge is:-

–1 g a
(A) tan (B) tan –1
a g
a a
(C) sin –1 (D) cos –1
g g g
(A) a =
cosec
2. In the arrangement shown in the figure, the g
(B) a =
block of mass m = 2 kg lies on the wedge sin 
on mass M = 8 kg. Find the initial (C) a = g cos 
acceleration of the wedge if the surfaces are (D) a = g tan 
smooth and pulley & strings are massless.

4. A car is moving on a plane inclined at 30°

to the horizontal with an acceleration of 10
m/s2 parallel to the plane upward. A bob is
suspended by a string from the roof. The
angle in degrees which the string makes
30 3 with the vertical is: (Assume that the bob
(A) a  m/s 2
23 does not move relative to car)
20 3 [g = 10 m/s2]
(B) a  m/s 2
23 (A) 20°

20 2 (B) 30°
(C) a  m/s 2
23 (C) 45°
(D) none of these (D) 60°

(14)
5. A cylinder rests in a supporting carriage as 7. A body of mass m is placed over a smooth
shown. The side AB of carriage makes an
inclined plane of inclination , which is
angle 30° with the horizontal and side BC
is vertical. The carriage lies on a fixed placed over a lift which is moving up with
horizontal surface and is being pulled an acceleration a0. Base length of the
towards left with an horizontal acceleration
‘a’. The magnitude of normal reactions inclined plane is L. Calculate the velocity
exerted by sides AB and BC of carriage on of the block with respect to lift at the
the cylinder be NAB and NBC respectively.
bottom, if it is allowed to slide down from
(Neglect friction everywhere). Then as the
magnitude of acceleration ‘a’ of the the top of the plane from rest.
carriage is increased, pick up the correct (A) 2(a0  g ) L sin 
statement:
(B) 2(a0  g ) L cos 

(C) 2(a0  g ) L tan 

(D) 2(a0  g ) L cot 

8. A block is sliding along inclined plane as

(A) NAB increases and NBC decreases.
shown in figure. If the acceleration of
(B) Both NAB and NBC increases.
chamber is ‘a’ as shown in the figure. The
(C) NAB remains constant and NBC
increases. time required to cover a distance L along
(D) NAB increases and NBC remains inclined plane is
constants.

6. A block of mass 2 kg slides down the face

of smooth 45° wedge of mass 9 kg as
shown in figure. The wedge is placed on a
frictionless horizontal surface. Determine
the acceleration (in m/s2) of the wedge.
(use g = 10 ms–2) 2L
(A)
g sin   a cos 

2L
(B)
g sin   a sin 

2L
(A) 2 m/s2 (C)
g sin   a cos 
11
(B) m/s 2
2 2L
(D)
(C) 1 m/s2 g sin 
(D) None of these

(15)
9. Two wooden blocks are moving on a 11. A block ‘A’ of mass ‘m’ is attached at one
smooth horizontal surface such that the end of a light spring and the other end of
mass m remains stationary with respect to spring is connected to another block ‘B’ of
block of mass M as shown in the figure. mass 2 m through a light string as shown in
The magnitude of force P is: the figure. ‘A’ is held and B is in static
equilibrium. Now A is released. The
acceleration of A just after that instant is
‘a’. In the next case, B is held and A is in
static equilibrium. Now when B is released,
its acceleration immediately after the
(A) (M + m) g tan  release is ‘b’. The value of a/b is: (Pully,
(B) g tan  string and the spring are massless)
(C) mg cos 
(D) (M + m) g cosec 

10. Two blocks of masses m1 and m2, which are

connected with light string, are placed over
a frictionless pulley. This set up is placed
over a weighing machine, as shown. Three
combination of masses m1 and m2 are used.
In first case m1 = 6 kg and m2 = 2 kg, in
(A) 0 (B) undefined
second case m1 = 5 kg and m2 = 3 kg and in
1
third case m1 = 4 kg and m2 = 4 kg. Masses (C) 2 (D)
2
are held stationary initially and then
released. If the reading of the weighing
12. Same spring is attached with 2 kg, 3 kg and
machine after the release in three cases are 1 kg blocks in three different cases as
W1, W2 and W3 then: shown in figure. If x1, x2 and x3 be the
extensions in the spring in these cases then
(Assume all the blocks to move with
uniform acceleration)

(A) W1 > W2 > W3 (B) W1 < W2 < W3 (A) x1 = 0, x3 > x2 (B) x2 > x1 > x3
(C) W1 = W2 = W3 (D) W1 = W2 < W3 (C) x3 > x1 > x2 (D) x1 > x2 > x3

(16)
13. The elevator shown in figure is descending 14. Assertion: Pseudo force is an imaginary
with an acceleration of 2 ms–2. The mass of force which is recognised only by a non-
the block A = 0.5 kg. The force exerted by inertial
the block A on the block B is observer to explain the physical situation
according to Newton's laws.
Reason: Pseudo force has no physical
origin, i.e., it is not caused by one of the
basic interactions in nature. It does not exist
in the action-reaction pair.
(A) Both Assertion & Reason are True &
the Reason is a correct explanation of
the Assertion.
(B) Both Assertion & Reason are True but
Take g = 10 m/s2 Reason is not a correct explanation of
(A) 4 N the Assertion.
(B) 8 N (C) Assertion is True but the Reason is
(C) 10 N False.
(D) 12 N (D) Both Assertion & Reason are False.

(17)
 DPP-7 (JPP/025)
[Friction as a contact force and coefficient of friction, Kinetic and
static friction, Angle of friction, Angle of repose]
1. The block of mass m is placed on a rough 4. If the coefficient of friction between an
horizontal floor and it is pulled by a ideal insect and bowl is  and the radius of the
string as shown by a constant force F. As bowl, is r, the maximum height to which
the block moves towards right the the insect can crawl in the bowl is:
frictional force on block-
r  
F (A) (B) r 1  1 
1  2
 1   2 

(C) r 1 2 (D) r 1  2  1
m
(A) remains constant (B) increases 5. Block B of mass 100 kg rests on a rough
(C) decreases (D) can be said surface of friction coefficient  = 1/3. A
rope is tied to block B as shown in figure.
2. A block rests on a rough plane whose The maximum acceleration with which
inclination  to the horizontal can be boy A of 25 kg can climbs on rope
varied. Which of the following graphs without making block move is
indicates how the frictional force F
between the block and the plane varies as
 is increased?

F
(A)
O 
90º

F F g 2g
(C) (D) (A) (B)
O  O  2 3
90º 90º
3g g
(C) (D)
3. Mark the correct statements about the 2 3
friction between two bodies -
(a) Static friction is always greater than 6. Determine the coefficient of friction (),
the kinetic friction so that rope of mass m and length l does
(b) Coefficient of static friction is
not slide down.
always greater than the coefficient
of kinetic friction
(c) Limiting friction is always greater
than the kinetic friction
(d) Kinetic friction is independent of
area of contact.
(A) b, c, d (B) a, b, c
(C) a, c, d (D) a, b, d

(18)
7. A worker wishes to pile a cone of sand 10. A block of mass 0.1 kg is held against a
into a circular area in his yard. The radius wall by applying a horizontal force of 5N
of the circle is r, and no sand is to spill on the block. If the Coefficient of friction
onto the surrounding area. If  is the
between the block and the wall is 0.5, the
static coefficient of friction between each
layer of sand along the slope and the magnitude of the frictional force acting
sand, the greatest volume of sand that can on the block is.
be stored in this manner is: (A) 2.5 N
r 3 r 3 (B) 0.98 N
(A) (B)
3 3 (C) 4.9 N
r 3 3 r 3 (D) 0.49 N
(C) (D)
3 
11. Statement-1
8. Find the magnitude of frictional force The maximum value of force F such that
between block A and table, if block A is the block shown in Fig, does not move is
pulled towards left with a force of 50N.
mg
, where  is the coefficient of
cos 
friction between the block and the
horizontal surface.
F


m
(A) 10 N
(B) 50 N
(C) 40 N Statement-2
(D) 30 N Frictional force = coefficient of friction 
normal reaction.
9. A thin rod of length 1m is fixed in a
(A) Statement-1 is true, Statement-2 is
vertical position inside a train, which is
moving horizontally with constant true and Statement-2 is the correct
acceleration 4 m/s2. A bead can slide on explanation for Statement-1.
the rod, and friction coefficient between (B) Statement-1 is true, Statement-2 is
them is 1/2. If the bead is released from true but Statement-2 is not the
rest at the top of the rod, find the time correct explanation for Statement-1.
when it will reach at the bottom.
(C) Statement-1 is true; Statement-2 is
(A) 0.5 second (B) 1 second
(C) 2 second (D) 2.5 second false.
(D) Both Statement-1 and Statement-2
are false.

(19)
12. A truck starting from rest moves with an
acceleration of 5 m/s2 for 1 sec and then
moves with constant velocity. The
velocity w.r.t. ground v/s time graph for
block in truck is (Assume that block does
not fall off the truck)
 = 0.2

(A)

(B)

(C)

(D) None of these

(20)
 DPP-8 (JPP/026)
[One or two blocks on inclined plane Blocks on rough horizontal
surface, Kinetic Friction and angle of repose]
1. A block of mass m is on an inclined plane 2. Two blocks each of mass 20 kg are
of angle θ. The coefficient of friction
connected by an ideal string and this
between the block and the plane is μ and
tanθ > μ. The block is held stationary by system is kept on rough horizontal
applying a force P parallel to the plane. surface as shown. Initially the string is
The direction of force pointing up the
just tight then a horizontal force F = 120
plane is taken to be positive. As P is
varied from P1 = mg(sinθ – μ cosθ) to P2 N is applied on one block as shown.
= mg(sinθ + μ cosθ), the frictional force f
20kgd 20kgd F=120N
versus P graph will be.

µ = 0.5 µ = 0.5
P
If friction coefficient at every contact is µ
 = 0.5 then which of the following
f represents the correct free body diagram.
P2 N=200N
N= 200N
P
(A) P1 T=50N T=50N
(A) 20kgd 20kgd F= 120N

f F1 = 50 N F2 = 70N
200N 200N

P N= 200N
N=200N
(B) P1 P2
T=20N T=20N
(B) 20kgd 20kgd F= 120N
f
F1 = 20 N F2 = 100N
P1 200N 200N
(C) P
P2 N=200N
N= 200N

T=60N T=60N
f (C) 20kgd 20kgd F= 120N

P1 P2 F1 = 60 N F2 = 60N
(D) P 200N 200N

(D) All of the above

(21)
3. Two blocks connected by a massless 5. A block is moving on an inclined plane
string slide down an inclined plane making an angle 45 with horizontal and
having angle of inclination 37º. The
masses of the two blocks are M1 = 4kg and the coefficient of friction is . the force
M2 = 2kg respectively and the coefficients required to just push it up the inclined
of friction are 0.75 and 0.25 respectively–
(a) The common acceleration of the two plane is 3 times the force required to just
masses is nearly 1.3 ms–2 prevent it from sliding down. If we define
(b) The tension in the string is nearly N = 10, then N is
14.7N
(c) The common acceleration of the two
masses is nearly 2.94 ms–2 6. In the figure, what should be mass m (in
(d) The tension in the string is nearly kg) so that block A slides up with a
5.29N
M1 = 4kg constant velocity.

M2 = 2kg

37º
A
(A) a, d (B) c, d kg m
(C) b, d (D) b, c 1 37°

4. A fixed wedge with both surface inclined  = 0.5

at 45 to the horizontal as shown in the
figure. A particle P of mass m is held on
7. A small mass slides down an inclined
the smooth plane by a light string which
passes over a smooth pulley A and plane of inclination  with the horizontal.
attached to a particle Q of mass 3m which The co-efficient of friction is  = 0x
rests on the rough plane. The system is
released from rest. Given that the where x is the distance through which the
acceleration of each particle is of mass slides down and 0, a constant.
g
magnitude then Then the distance covered by the mass
5 2
before it stops is:
2
(A) tan 
0
4
(B) tan 
0
(a) The tension in the string is: 1
(C) tan 
6mg 2 0
(A) mg (B)
5 2 1
mg mg (D) tan 
(C) (D) 0
2 4

(22)
8. A block placed on a rough inclined plane 11. A wedge of mass 2 m and a cube of mass
of inclination ( =30) can just be pushed m are shown in figure. Between cube and
upwards by applying a force "F" as wedge, there is no friction. The minimum
shown. If the angle of inclination of the
coefficient of friction between wedge and
inclined plane is increased to ( = 60),
the same block can just be prevented ground so that wedge does not move is:
from sliding down by application of a
force of same magnitude. The coefficient
of friction between the block and the
inclined plane is

F
(A) 0.20

(B) 0.25
3 1 2 3 1 (C) 0.10
(A) (B)
3 1 3 1 (D) 0.50
3 1
(C) (D) None of these
3 1 12. Statement 1: A block of mass m is
placed on smooth fixed inclined plane of
9. A block of mass 'M' is slipping down on
a rough incline of inclination  with inclination  with the horizontal. The
horizontal with a constant velocity. The force exerted by the plane on the block
magnitude and direction of total reaction has a magnitude mg cos .
from the inclined plane on the block is :
Statement 2: Normal reaction always
(A) Mg sin  down the incline
acts perpendicular to the contact surface.
(B) less than Mg sin  down the incline
(C) Mg upwards (A) Statement-1 is true, Statement-2 is
(D) Mg downwards true and Statement-2 is the correct
explanation for Statement-1.
10. A block kept on an inclined surface, just (B) Statement-1 is true, Statement-2 is
begins to slide if the inclination is 30.
true but Statement-2 is not the
The block is replaced by another block B
and it just begins to slide if the inclination correct explanation for Statement-1.
is 40, then: (C) Statement-1 is true; Statement-2 is
(A) Mass of A > mass of B false.
(B) Mass of A < mass of B (D) Statement-1 is false; Statement-2 is
(C) Mass of A = mass of B
true.
(D) All the three are possible

(23)
 DPP-9 (JPP/027)

[Block Over Block Problems]

1. For the system shown find the maximum 4. Two masses A and B of 10 kg and 5kg
value of F so that A does not slip on B. respectively are connected with a string
passing over a frictionless pulley fixed at
the corner of a table as shown in figure.
The coefficient of friction of A with the
table is 0.2. The minimum mass of C that
may be placed on A to prevent it from
(A) 10 N
moving is equal to:
(B) 5N
(C) 6N C
(D) 12 N 10 kg
A
2. Find the friction acting between the
blocks.
5 kg
B
(A) 8 N
(B) 6 N
20 (A) 15 kg (B) 10 kg
(C) N (C) 5 kg (D) Zero
3
(D) 4 N
5. Block M slides down on frictionless
3. A block A with mass 100 kg is resting on incline as shown. Find the minimum
another block B of mass 200 kg. As friction coefficient so that m does not
shown in figure a horizontal rope tied to
slide with respect to M.
a wall holds it. The coefficient of friction
between A and B is 0.2 while coefficient
of friction between B and the ground is
0.3. The minimum required force F to
start moving B will be

3
(A)
4
4
(A) 900 N (B)
5
(B) 100 N
(C) 1100 N (C) 2
(D) 1200 N (D) 0

(24)
6. A block A of mass 2kg rests on another 9. When a horizontal force is applied on the
block B of mass 8kg which rests on a
bottom block, the accelerations of the
horizontal floor. The coefficient of
friction between A and B is 0.2 while that blocks (in m s2) are (starting from top) 1,
between B and floor is 0.5. When a
2 and 3 respectively (g = 10 m s2)
horizontal force F of 25N is applied on
the block B, the force of friction between 3m 0 Initially
A and B is _________N.
2m 0 at rest
7. Given mA = 30 kg, mB= 10 kg, mC = 20 m = 0
kg. Between A & B 1 = 0.3, between B
& C 2 = 0.2 & between C & ground 3 =  between m and 2 m is
0.1. The least horizontal force F to start
motion of any part of the system of three (A) 0.14
blocks resting upon one another as shown (B) 0.23
below is:
(Take g = 10 m/s2) (C) 0.32
A F (D) 0.41
B
C 10. Statement-1: It is found that the two
bodies shown are moving as a single unit,
(A) 90 N (B) 80 N
(C) 60 N (D) 150 N there must be external force(s) acting on
either or both bodies horizontally, or
8. Consider the situation shown in figure in
having a horizontal component.
which a block ‘A’ of mass 2 kg is placed
over a block ‘B’ of mass 4 kg. The Statement-2: When an opposing force is
combination of the blocks are placed on present, motion is possible only when an
a inclined plane of inclination 37 with
horizontal and coefficient of friction external force overcomes it.
between B and inclined plane is 2. The
coefficient of friction between blocks is
1. The system is released from rest.
(Take g = 10 m/s2)
(A) Statement-1 is true, Statement-2 is
true and Statement-2 is the correct
explanation for Statement-1.
(B) Statement-1 is true, Statement-2 is
true but Statement-2 is not the
If 1  0.8, 2  0.8 then: correct explanation for Statement-1.
(A) both blocks will move together (C) Statement-1 is true; Statement-2 is
(B) only block A will move and block B
remains at rest false.
(C) Only block B will move and block A (D) Statement-1 is false; Statement-2 is
remains at rest
(D) None of the blocks will move true.

(25)
 DPP-10 (JPP/028)

[Acceleration in Circular motion, Dynamics of Circular Motion]

1. A person with a mass of M kg stands in 4. In circular motion of a particle the
contact against the wall of the cylindrical tangential acceleration of the particle is
drum of radius r rotating with an angular
given by at = 2t m/s2. The radius of the
velocity . The coefficient of friction
between the wall and the clothing is . circle described is 4m. The particle is
The minimum rotational speed of the initially at rest. Time after which net
cylinder which enables the person to force on the particle makes 45 with
remain stuck to the wall when the floor is
radial acceleration is:
suddenly removed is -
(A) 1 sec
g r
(A) min = (B) min = (B) 2 sec
r g
(C) 3 sec
2g gr
(C) min = (D) min = (D) 4 sec
r 

2. A uniform rod of mass m and length L is 5. In the figure, the spring is horizontal, its
rotated with angular speed  about axis natural length is l and gravity is absent if
AA' as shown in figure. The tension in the the spring is whirled with an angular
rod at a distance of 3L from the axis is speed , what is the new length of the
4
spring ?

3m2 L m2 L
(A) (B)
4 8 𝑚𝜔2 𝑙 𝑚𝜔2 𝑙
(A) (B)
𝑘+𝑚𝜔2 𝑘−𝑚𝜔2
7m2 L 7m2 L 𝑘𝑙 𝑘𝑙
(C) (D) (C) (D)
32 8 𝑘+𝑚𝜔2 𝑘−𝑚𝜔2

6. A particle of mass m rotates about Z-axis

3. A stone is thrown horizontally with a
in a circle of radius a with a uniform
velocity of 10 m/s at t = 0. The radius of
curvature of the stone’s trajectory at t = 3 angular speed . It is viewed from a
s is: frame rotating about the same Z-axis with
[Take g = 10 m/s2] a uniform angular speed 0. The
(A) 10 10 m centrifugal force on the particle is :

(B) 100 m (A) m2 a (B) m02 a

   0 
2
(C) 100 10 m
(C) m   a (D) m0 a
(D) 1000 m  2 

(26)
7. A particle of mass m1 is fastened to one 9. If a particle starts from A along the
end of a massless string and another curved circular path shown in figure with
particle of mass m2 is fastened to the tangential acceleration ‘a’. Then
middle point of the same string. The other acceleration at B in magnitude is :
end of the string being fastened to a fixed B
point on a smooth horizontal table. The
particles are then projected, so that the
two particles and the string are always in A C
the same straight line and describe
(A) 2a 1 2 (B) a 1 2
horizontal circles. Then, the ratio of
tensions in the inner string to the outer (C) a 2  1 (D) a 1  2
string is :
(A) m1 /  m1  m2  10. A particle P is attached by means of two
equal strings to two points A and B in
(B)  m1  m2  / m1 same vertical line and describes
(C)  2m1  m2  / 2m1 horizontal circle with uniform angular
(D) 2m1 /  m1  m2  speed 2
2g
where AB = h.
h
8. Indicate the direction of frictional force 
on a car which is moving along the
A
T1
curved path with non-zero tangential
acceleration; in anti-clock direction: h P
f
T2
(A) f (B) B
(A) T1 : T2 = 9 : 7
(B) T1 : T2 = 5 : 3
f
(C) (D) (C) T1 : T2 = 5: 3
(D) T1 = T2

(27)
 DPP-11 (JPP/029)
[Dynamics of circular motion and Banking of road and conical
pendulum]
1. A simple pendulum is made of bob of 3. A block of mass m is placed at the top of
mass m and using string of length L fixed a smooth wedge ABC. The wedge is
rotated about an axis passing through C
at upper end. The bob oscillates in
as shown in the figure. The minimum
vertical circle. It is found that speed of value of angular speed  such that the
the bob is v when the string makes an block does not slip on the wedge is-

angle  with the vertical. The tension T A m
at this instant is- 
(A) T = mg cos 
B  C
2
mv
(B) T = mg cos  –
L  g sin    g
(A)   sec 
 (B)   cos 

    
mv 2
(C) T =
L  g  g sin 
(C)  
cos  (D)
mv 2   cos   
(D) T = mg cos  +
L
4. A small body of mass m can slide without
2. A motor cyclist moving with a velocity of friction along a trough bend which is in
the from of a semi-circular arc of radius
72 km per hour on a flat road takes a turn
R. At what height h will the body be at
on the road at a point where the radius of rest with respect to the trough, if the
curvature of the road is 20 meters. The trough rotates with uniform angular
velocity  about a vertical axis:
acceleration due to gravity is 10 m/s2. In

order to negotiate the turn, he must bend
at an angle of,
h
(A)  = tan–1 6
2g
(B)  = tan–1 2 (A) R (B) R 
2
(C)  = tan 25.92
–1
2g g
(C) R  (D) R 
(D)  = tan 4–1  2
2

(28)
5. A curved section of road is banked for a 8. A body moves on a horizontal circular
speed v. If there is no friction between the road of radius r, with a tangential
road and the tyres then: acceleration aT. Coefficient of friction
(A) a car moving with speed v does not between the body and road surface is .
slip on the road It begins to slip when it’s speed is v, then:
(B) a car is more likely to slip on the
road at speed higher than v, than at (A) v2  rg
speeds lower than v v2
(C) a car is more likely to slip on the (B) g   aT
r
road at speeds lower than v, than at
speeds higher than v (C) The force of friction makes an angle
(D) a car can remain stationary on the
 a r 
road with slipping tan 1  T 2  with direction of
 v 
6. A particle of mass m is attached to one motion at point of slipping.
end of a string of length l while the other 4
v
end is fixed to point h (h < l) above a (D)  2 g 2   aT2
r2
horizontal table. The particle is made to
revolve in a circle on the table so as to
9. A horizontal rod AB of length 1 m, with a
make p revolutions per second. The
maximum value of p, if the particle is to 1 m long light, inextensible string with a
be in contact with the table, is: (l > h) bob attached to it and suspended from
1 end B is rotated on the horizontal plane
(A) h/ g about point A at a constant angular
2
velocity of 10 rad s–1 so that the string
(B) g/h
makes angle  with vertical. (g = 10 m s–
(C) 2 h / g 2
)  lies between
1 B
(D) g/h A
2

7. A smooth hollow cone whose vertical
angle is 2 with its axis vertical and
vertex downwards revolves about its axis
time per seconds. A particle is placed on (A) 0° and 30° (B) 30° and 45°
the inner surface of cone so that it rotates (C) 45° and 65° (D) 65° and 90°
with same speed. The radius of rotation
for the particle is: 10. A car of mass 1000 kg negotiates a
(A) g cot  / 4 
2 2 banked curve of radius 90 m on a
frictionless road. If the banking angle is
(B) g sin  / 422
45°, the speed of the car is:
(C) 422 / g (A) 20 ms–1 (B) 30 ms–1
(D) g / 422 sin  (C) 5 ms–1 (D) 10 ms–1

(29)